# An $\ell $-algebra approach to Artin’s solution of Hilbert’s Seventeenth Problem

Stuart A. Steinberg^{[1]}

- [1] The University of Toledo Toledo, Ohio, U.S.A.

Annales de la faculté des sciences de Toulouse Mathématiques (2010)

- Volume: 19, Issue: S1, page 215-220
- ISSN: 0240-2963

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topSteinberg, Stuart A.. "An $\ell $-algebra approach to Artin’s solution of Hilbert’s Seventeenth Problem." Annales de la faculté des sciences de Toulouse Mathématiques 19.S1 (2010): 215-220. <http://eudml.org/doc/115898>.

@article{Steinberg2010,

abstract = {Using lattice-ordered algebras it is shown that a totally ordered field which has a unique total order and is dense in its real closure has the property that each of its positive semidefinite rational functions is a sum of squares.},

affiliation = {The University of Toledo Toledo, Ohio, U.S.A.},

author = {Steinberg, Stuart A.},

journal = {Annales de la faculté des sciences de Toulouse Mathématiques},

keywords = {lattice-ordered algebra; Hilbert's seventeenth problem},

language = {eng},

month = {4},

number = {S1},

pages = {215-220},

publisher = {Université Paul Sabatier, Toulouse},

title = {An $\ell $-algebra approach to Artin’s solution of Hilbert’s Seventeenth Problem},

url = {http://eudml.org/doc/115898},

volume = {19},

year = {2010},

}

TY - JOUR

AU - Steinberg, Stuart A.

TI - An $\ell $-algebra approach to Artin’s solution of Hilbert’s Seventeenth Problem

JO - Annales de la faculté des sciences de Toulouse Mathématiques

DA - 2010/4//

PB - Université Paul Sabatier, Toulouse

VL - 19

IS - S1

SP - 215

EP - 220

AB - Using lattice-ordered algebras it is shown that a totally ordered field which has a unique total order and is dense in its real closure has the property that each of its positive semidefinite rational functions is a sum of squares.

LA - eng

KW - lattice-ordered algebra; Hilbert's seventeenth problem

UR - http://eudml.org/doc/115898

ER -

## References

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- K. McKenna, New facts about Hilbert’s seventeenth problem, Lecture Notes in Mathematics 498, Model theory and algebra, A memorial tribute to Abraham Robinson, 1975, 220–230. Zbl0357.12019MR401720
- A. Pfister, Hilbert’s seventeenth problem and related problems on definite forms, Mathematical developments arising from Hilbert problems, Proceedings of symposia in pure mathematics 28, part 2, Amer. Math. Soc., Providence, 1976, 483–489. Zbl0337.12101MR424679
- A. Prestel and C. N. Delzell, Positive polynomials, Springer, Berlin, 2001. Zbl0987.13016MR1829790
- E. C. Weinberg, Lectures on ordered groups and rings, University of Illinois, Urbana, 1968.
- E. C. Weinberg, University of Illinois seminar, 1971.

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